Methods for optimal gradient design and fast generic waveform switching

ABSTRACT

This disclosure provides a computer-implemented method for sequencing magnetic resonance imaging waveforms using a multistage sequencing hardware. The method comprises creating, with the aid of a computer processor, an active memory region that includes waveforms and schedules being played, and creating one or more buffer memory regions that contain waveforms and schedules not currently being played. Next, the waveforms and schedules in the one or more buffer memory regions may be updated while waveforms may be played in the active memory region. Upon completion of the waveform playback in the active memory region, the active and buffer memory regions may be swapped so that the former buffer memory region becomes the active memory region, and the former active memory region becomes the buffer memory region. The method may be repeated as needed until the imaging process is completed or otherwise halted.

CROSS-REFERENCE

This application is a continuation of U.S. patent application Ser. No.14/640,685, filed Mar. 6, 2015, now U.S. patent Ser. No. __/______;which is a continuation of PCT/US13/21077 filed on Jan. 10, 2013; whichclaims the benefits of U.S. Provisional Patent Application No.61/698,522, filed Sep. 7, 2012; and U.S. Provisional Patent ApplicationNo. 61/698,504, filed Sep. 7, 2012; the full disclosures of which areentirely incorporated herein by reference.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with the support of the United States governmentunder contract numbers R44HL084769 and R44HL092691 by the NationalInstitutes of Health. The government has certain rights in theinvention.

BACKGROUND

The present disclosure relates generally to medical devices and methods.Although specific reference is made to magnetic resonance imaging (MRI),the methods and apparatus described herein can be used with many medicalimaging and diagnostic procedures and apparatuses.

Magnetic resonance imaging (MRI) relies on the principles of nuclearmagnetic resonance (NMR). In MRI, an object to be imaged is placed in auniform magnetic field (B₀), subjected to a limited-duration magneticfield (B₁) perpendicular to B₀, and then signals are detected as the“excited” nuclear spins in the object “relax” back to their equilibriumalignment with B₀ following the cessation of B₁. Through the applicationof additional magnetic fields (“gradients”) to the imaging process,detected signals can be spatially localized in up to three dimensions.

MRI of living subjects generally makes use of water protons found intissues. In a typical imaging setup, a subject may then be first placedin a uniform magnetic field (B₀), where the individual magnetic momentsof the water protons in the subject's various tissues align along theaxis of B₀ and precess about it at the so-called Larmor frequency. Theimaged subject may then be exposed to a limited-duration “excitation”magnetic field (B₁, generally created by application of aradio-frequency (RF) “pulse”) perpendicular to B₀ and at the Larmorfrequency, where the net aligned magnetic moment (the sum of allindividual proton moments aligned with B₀) at equilibrium, m₀, istemporarily rotated, or “tipped” toward the plane corresponding to B₁(the “transverse” plane). This results in the formation of a net moment,m_(t), in the transverse plane. After cessation of B₁, a signal may berecorded from m_(t) as it “relaxes” back to m₀. The local magnetic fieldenvironment of each tissue affects m_(t) relaxation rates uniquely,resulting in tissue differentiation on images. Moreover, magnetic fieldgradients are typically employed in order to spatially localize thesignals recorded from m_(t). The excitation/gradient application/signalreadout process, a so-called “pulse sequence”, may be performedrepetitively in order to achieve appropriate image contrast. Theresulting set of received signals may then be processed withreconstruction techniques to produce images useful to the end-user.

Advances in the field of Magnetic Resonance Imaging (MRI), such asgradient hardware, high field systems, optimized receiver coil arrays,fast sequences and sophisticated reconstruction methods, provide theability to perform rapid MRI imaging. In at least some instances,however, the capabilities of an MRI machine may be limited by memorycapacity and processing speed. Improved methods and apparatuses forperforming rapid MRI imaging, particularly in a memory and processingpower limited MRI machine, are therefore desired.

Time-efficient production of time-optimal gradient waveforms that complywith safety and hardware gradient rate-of-change limitations isgenerally recognized as an important challenge for real-time MRI. Whileother methods may adequately calculate time-efficient gradient waveformsthat conform to hardware and safety rate-of-change limitations, they maytake many minutes to compute, and may render them unusable for real-timeimaging. Thus, improved methods and apparatuses for providing moretime-efficient gradient waveforms that conform to hardware and safetyrate-of-change limitations in MRI machines are desired.

SUMMARY

In an aspect, this disclosure provides a method that generatestime-efficient linear magnetic field gradient waveforms that may producemagnetic field gradient pulses that come within 10% or better of theregulatory and/or hardware limit and may need only milliseconds tocompute is provided. Moreover, the method may also be extended to designof specific k-space trajectories, non-linear magnetic field gradients,and new pulse sequence applications such as the optimization method ofthe disclosure, where the gradient area, moment, and start/endamplitudes may be the desired input parameters.

This disclosure provides systems and methods for graphically orprogrammatically creating pulse sequences based upon parameters relevantto the MRI pulse-sequence designer are provided. Many current magneticresonance imaging (MRI) scanners require the pulse-sequence designer toindependently determine and design the shapes of gradient waveforms thatmeet certain desired requirements, and only provide certain primitivestructures such as trapezoids and ramps to help accomplish this design.Typically, an MRI pulse-sequence designer desires a certain gradientarea and/or moment to be realized on one or more gradient axes, withgiven start and end amplitudes, rather than be interested in thespecific shape of the waveform for most applications. Matching designtools to these user needs can greatly improve the ability to design newMRI acquisition strategies with a minimum of designer effort and time.

Real-time MRI may also require that sets of arbitrary waveforms andplayback schedules be rapidly uploaded into a piece of dedicatedmagnetic resonance (MR) sequencing hardware that may be limited inprocessing power and/or available memory. Parameters of these waveformssuch as their durations, amplitudes, data points, and number may allchange arbitrarily and may not be known ahead of time.

This disclosure also provides a method for generating magnetic fieldgradients used in magnetic resonance imaging (MRI). With the aid of acomputer processor, a set of gradient parameters is geometricallytransformed from a physical gradient space into a geometricallytransformed space (e.g., with at least one of a rotative transformation,a proportional transformation, a magnitude transformation, etc.). Withthe aid of a computer processor, a set of separable gradient waveformsthat satisfy a set of gradient rate-of-change constraints in thegeometrically transformed space is calculated. The set of gradientparameters may contain parameters that include a gradient startmagnitude, gradient end magnitude, gradient amplitude, gradient firstmoment, and higher-order gradient moments. At least two of theseparameters may typically be used. The set of rate-of-change constraintsmay comprise one or more of a physical hardware constraint and aregulatory safety constraint. The geometric transforming and calculatingsteps are repeated until the gradient waveforms in the set of separablegradient waveforms are of substantially the same time length. This stepof repetition may be a nonlinear solution method. With the aid of acomputer processor, the resulting gradient set of waveforms ofsubstantially the same time length is geometrically transformed backinto the physical gradient space.

This disclosure also provides methods for rapidly and efficientlyuploading arbitrary waveforms and playback schedules into a piece ofsequencer hardware (e.g., MRI hardware) at any point, including duringsequence execution, while minimizing playback time, system processing,and data storage requirements. When schedules are created in this way,preparation processing time can be reduced from many seconds tomilliseconds or less. When preparation times cross the importantthreshold of requiring roughly less processing time than about thesequence repetition time (TR), which may be as short as a fewmilliseconds, sequences can be prepared just-in-time during sequenceexecution. This just-in-time sequence preparation enables true real-timemanipulation of the imaging acquisition in arbitrary ways with littleperceptible latency between action and reaction. Moreover, memoryrequirements for alternative schedules can be reduced by an order ofmagnitude through storing only the current and next iterations at anygiven time.

For example, a method for sequencing waveforms used in magneticresonance imaging (MRI) may be provided. An active memory region and onor more buffer memory regions in a computer-readable medium areprovided. The active memory region comprises one or more waveforms andschedules being played while the one or more buffer regions comprise oneor more waveforms and schedules not currently being played. With the aidof a computer processor, the one or more waveforms and schedules notcurrently being played in the one or more buffer memory regions areupdated while the one or more waveforms and schedules of the activememory region are being played. Upon the completion of the waveformplayback in the active memory region, the active memory region and thebuffer memory region are swapped with the aid of a computer processor.This swapping may occur without sequencer inactivity or delay. Thesesteps are repeated until the imaging process is complete.

The waveforms of the active memory region and the one or more bufferregions may comprise at least one gradient waveform, RF channelwaveform, shim waveform, field waveform, or acoustic waveform. Theschedules of the active memory region and the one or more buffer regionsmay comprise pointers to at least one waveform region, duration,amplitude, or delay interval. The waveform playback may comprise a timeinterval per iteration which may vary from one iteration to another.

Updating the one or more waveforms and schedules not being played in theone or more buffer memory regions may comprise two or more steps. Theone or more waveforms and schedules not being played are subdivided intoone or more blocks that represent sequencing regions that areindependently modifiable. Real-time changes are performed on individualblocks. Such real-time changes comprise one or more of scaling,rotation, enabling, and disabling.

This disclosure also provides a method for permitting real-time changesto waveforms used in magnetic resonance imaging (MRI). A time intervalis subdivided into one or more blocks that represent sequencing regionsthat are independently modifiable. Real-time changes are performed onindividual blocks. Such real-time changes comprise one or more ofscaling, rotation, enabling, and disabling.

This disclosure also provides a method of generating a waveform used inimaging applications. A first combined constraint for an imaging deviceis determined by calculating, with the aid of a computer processor, anintersection between a first multidimensional limitation and a secondmultidimensional limitation. The first multidimensional limitation maycomprise a hardware limitation for an imaging device such as a gradientamplitude limit or a gradient slew rate limit. The gradient amplitude orslew-rate limit may be calculated as a peak or as a root-mean-squarelimit. The second multidimensional limitation may comprise a regulatorylimitation for an imaging device such as a maximum safe rate of changefor a magnetic field for a scan subject. The regulatory limitation maycomprise a maximum safe rate of change of a magnetic field for a scansubject in the presence of an implantable or interventional medicaldevice. A set of desired gradient properties is provided. These gradientproperties may include at least one or two of a starting gradientmagnitude, an ending gradient magnitude, a net gradient area, and ahigher-order gradient moment. A set of desired multidimensional gradientparameters in a first coordinate space is calculated from the providedset of desired gradient properties. The calculated set of desiredmultidimensional gradient parameters is geometrically transformed into asecond coordinate space. A second combined constraint for the imagingdevice is determined by calculating an intersection between the firstcombined constraint and the geometrically transformed set of desiredmultidimensional gradient parameters. A multidimensional set of gradientwaveforms that satisfy the second combined constraint is calculated. Themultidimensional set of gradient waveforms will comprise a firstwaveform in a first axis, a second waveform in a second axis, and oftenalso a third waveform in a third axis. It is then determined whether thefirst waveform, second waveform, and often the third waveform have thesame time length. If the waveforms have the same time length, themultidimensional set of gradient waveforms is geometrically transformedback into the first coordinate space. If the waveforms do not have thesame time length, many of the above steps may be repeated until they do.A magnetic field gradient pulse for a Magnetic Resonance Imaging (MRI)device or scanner can then be generated based on the geometricallytransformed multidimensional set of gradient waveforms.

This disclosure also provides a method of generating waveforms used inan imaging application. A first imaging waveform is generated based on afirst waveform schedule read from a first memory region in a computerreadable medium. A second waveform schedule in a second memory region inthe computer readable medium is updated while the first imaging waveformis being generated. A second imaging waveform is generated based on thesecond waveform schedule read from the second memory region after thefirst imaging waveform has finished being generated. The first imagingwaveform schedule in the first memory region is updated while the secondimaging waveform is being generated. The first waveform schedule and thesecond waveform schedule may be comprised of least one gradientwaveform, RF channel waveform, shim waveform, field waveform, oracoustic waveform. The first waveform schedule and the second waveformschedule may comprise pointers to at least one waveform region,duration, amplitude, or delay interval. The time interval for generatingthe first imaging waveform may be the same as the time interval forgenerating the second imaging waveform. There may be no time delaybetween generating the first imaging waveform and generating the secondimaging waveform.

This disclosure also provides a computer-readable medium comprising codewhich, when executed by a computer processor, executes a method. In afirst step of this method, a set of gradient parameters from a physicalgradient space is geometrically transformed, with the aid of a computerprocessor, into a geometrically transformed space (e.g., with at leastone of a rotative transformation, a proportional transformation, amagnitude transformation, etc.). In a second step, a set of separablegradient waveforms that satisfy a set of gradient rate-of-changeconstraints in said geometrically transformed space is calculated, withthe aid of a computer processor. In a third step, the first and secondsteps are repeated until the gradient waveforms in said set of separablegradient waveforms are of substantially the same time length. In afourth step, a resulting gradient set of waveforms of substantially thesame time length is geometrically transformed, with the aid of acomputer processor, back into said physical gradient space.

This disclosure also provides a computer-readable medium comprising codewhich, when executed by a computer processor, executes a method. In afirst step, an active memory region in a memory location of a computersystem programmed to sequence MRI waveforms is provided. The activememory region comprises one or more waveforms and schedules beingplayed. In a second step, one or more buffer memory regions in thememory location is provided. The one or more buffer regions comprise oneor more waveforms and schedules not currently being played. In a thirdstep, the one or more waveforms and schedules not currently being playedin said one or more buffer memory regions is updated, with the aid of acomputer processor of said computer system, while said one or morewaveforms and schedules of said active memory region are being played.In a fourth step, said active memory region is swapped with said buffermemory region with the aid of a computer processor upon completion ofthe waveform playback in said active memory region.

This disclosure also provides a computer-readable medium comprising codewhich, when executed by a computer processor, executes a method. In afirst step of the method, a time interval of a magnetic resonanceimaging waveform is subdivided, with the aid of a computer processor,into one or more blocks that represent sequencing regions that areindependently modifiable. In a second step, real-time changes areperformed on individual blocks. The real-time changes comprise one ormore of scaling, rotation, enabling, and disabling.

This disclosure also provides a computer-readable medium comprising codewhich, when executed by a computer processor, executes a method. In afirst step of the method, a first imaging waveform is generated based ona first waveform schedule read from a first memory region of a memorylocation of a computer system programmed to generate waveforms. In asecond step, a second waveform schedule in a second memory region in amemory location is updated while the first imaging waveform is beinggenerated. In a third step, a second imaging waveform is generated basedon the second waveform schedule read from the second memory region whenthe first imaging waveform has been generated. In a fourth step, thefirst imaging waveform schedule in the first memory region is updated.

This disclosure also provides a system for generating magnetic fieldgradients for use in magnetic resonance imaging (MRI). The systemcomprises a computer processor and a memory location coupled to thecomputer processor. The memory location comprises code which, whenexecuted by said computer processor, implements a method. In a firststep of this method, a set of gradient parameters is geometricallytransformed, with the aid of a computer processor, from a physicalgradient space into a geometrically transformed space (e.g., with atleast one of a rotative transformation, a proportional transformation, amagnitude transformation, etc.). In a second step, a set of separablegradient waveforms that satisfy a set of gradient rate-of-changeconstraints in said geometrically transformed space is calculated, withthe aid of a computer processor. In a third step, the first and secondsteps are repeated until the gradient waveforms in said set of separablegradient waveforms are of substantially the same time length. In afourth step, a resulting gradient set of waveforms of substantially thesame time length is geometrically transformed back into said physicalgradient space.

This disclosure also provides a system for sequencing waveforms for usein magnetic resonance imaging (MRI). The system comprises a computerprocessor and a memory location coupled to the computer processor. Thememory location comprises code which, when executed by said computerprocessor, implements a method. In a first step of this method, anactive memory region in a memory location of a computer systemprogrammed to sequence MRI waveforms is provided. The active memoryregion comprises one or more waveforms and schedules being played. In asecond step, one or more buffer memory regions in the memory location isprovided. The one or more buffer regions comprise one or more waveformsand schedules not currently being played. In a third step, the one ormore waveforms and schedules not currently being played in said one ormore buffer memory regions is updated, with the aid of a computerprocessor of said computer system, while said one or more waveforms andschedules of said active memory region are being played. In a fourthstep, the active memory region is swapped with the buffer memory regionupon completion of the waveform playback, with the aid of a computerprocessor.

This disclosure also provides a system for permitting real-time changesto waveforms used in magnetic resonance imaging (MRI). The systemcomprises a computer processor and a memory location coupled to thecomputer processor. The memory location comprising code which, whenexecuted by said computer processor, implements a method. In a firststep of the method, a time interval of a magnetic resonance imagingwaveform is subdivided, with the aid of a computer processor, into oneor more blocks that represent sequencing regions that are independentlymodifiable. In a second step, real-time changes on individual blocks areperformed. These real-time changes comprise one or more of scaling,rotation, enabling, and disabling.

This disclosure also provides a system for generating magnetic fieldgradients for use in magnetic resonance imaging (MRI). The systemcomprises a computer processor and a memory location coupled to thecomputer processor. The memory location comprises code which, whenexecuted by said computer processor, implements a method. In a firststep of the method, a set of gradient parameters is geometricallytransformed, with the aid of a computer processor, from a physicalgradient space into a geometrically transformed space (e.g., with atleast one of a rotative transformation, a proportional transformation, amagnitude transformation, etc.). In a second step, a set of separablegradient waveforms that satisfy a set of gradient rate-of-changeconstraints in said geometrically transformed space is calculated. In athird step, the first and second steps are repeated until the gradientwaveforms in said set of separable gradient waveforms are ofsubstantially the same time length. In a fourth step, a resultinggradient set of waveforms of substantially the same time length isgeometrically transformed back into said physical gradient space.

This disclosure also provides a system for generating waveforms for usein an imaging application. The system comprises a computer processor anda memory location coupled to the computer processor. The memory locationcomprises code which, when executed by said computer processor,implements a method. In a first step of the method, a first imagingwaveform based on a first waveform schedule read from a first memoryregion of a memory location of a computer system programmed to generatewaveforms is generated. In a second step, a second waveform schedule ina second memory region in a memory location is updated while the firstimaging waveform is being generated. In a third step, a second imagingwaveform is generated based on the second waveform schedule read fromthe second memory region when the first imaging waveform has beengenerated. In a fourth step, the first imaging waveform schedule in thefirst memory region is updated.

Additional aspects and advantages of the present disclosure will becomereadily apparent to those skilled in this art from the followingdetailed description, wherein only illustrative embodiments of thepresent disclosure are shown and described. As will be realized, thepresent disclosure is capable of other and different embodiments, andits several details are capable of modifications in various obviousrespects, all without departing from the disclosure. Accordingly, thedrawings and description are to be regarded as illustrative in nature,and not as restrictive.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings of which:

FIG. 1 schematically illustrates a two-dimensional example of the safetyand hardware limitations for maximum magnetic field gradientrates-of-change permitted in MRI. The areas where permitted safety andhardware areas overlap represent the space of allowable rates ofmagnetic field gradient rates-of-change and thus define the maximumrange of possible slew rates.

FIG. 2 shows an example of a design process wherein an efficientCartesian readout gradient is designed with specified areas, startamplitudes, and end amplitudes.

FIG. 3 is a flow chart of an exemplary process described herein for thedesign of time-efficient gradient waveforms.

FIG. 4 describes an exemplary set of simplifying geometrictransformation and rotation elements of the present invention used tocalculate time-optimal magnetic field gradient waveforms in atwo-dimensional example. In (a) (b) and (c), physical gradient axes (Gx,Gy) and logical gradient axes (Gx′, Gy′) overlap. In (d) (e) and (f,these coordinate systems differ. In (a) and (d), an additional rotationis introduced to create a geometrically transformed space in which toapply separable gradient design techniques. Alternatively, (b) and (e)show a proportional approach that can be applied to provide analternative separable geometric transform space. Finally, (c) and (f)show a magnitude-based simplifying geometric transform that is notseparable but nonetheless can simplify some designs. In each case, theshaded region indicates a combined, simplified safety/hardwareconstraint in the geometrically transformed space.

FIG. 5 describes physical magnetic field gradient waveforms calculatedas a function of time using the present invention in a three-dimensionalexample.

FIG. 6 describes the point-wise magnetic field gradient change limits ofthe waveforms shown in FIG. 5. The average data point is at 93% of thetheoretical limit.

FIG. 7 is a conceptual schematic describing the computer memoryarchitecture that may be used in MRI sequencing hardware. A schedulerfor each waveform axis plays waveforms uploaded into a waveform library.The scheduler may make simple transformations such as bulk amplitudechanges, duration changes, phase/rotation changes, or changes to whichwaveform in the library the scheduler may be pointing.

FIG. 8a schematically shows a waveform sequence execution from hardwarecomputer memory. Waveforms may be played from computer memory using thescheduler. Following playback, the scheduler may be serially updated inthe computer memory during a period of waveform inactivity. Theswitching of waveform sequence playback and scheduler update may repeatuntil an imaging sequence is completed. FIG. 8b schematically depicts awaveform sequence of the invention. Waveforms may be played in an activememory region while the required updates to both the waveform libraryand scheduler for a future sequencing interval (TR) may be concurrentlyuploaded into a separate buffer region. The active region may be swappedwith the buffer region corresponding to the next TR and that bufferregion then may be played as the new active region, whereas the formeractive region may now function as a buffer region for a subsequentplayback period.

FIG. 9 shows a single TR of a spiral flow-encoded pulse sequence showingan example of how a TR interval may be divided into three distinctblocks.

FIG. 10 schematically illustrates a computer system that may beprogrammed to implement methods of the disclosure.

DETAILED DESCRIPTION

While various embodiments of the invention have been shown and describedherein, it will be obvious to those skilled in the art that suchembodiments are provided by way of example only. Numerous variations,changes, and substitutions may occur to those skilled in the art withoutdeparting from the invention. It should be understood that variousalternatives to the embodiments of the invention described herein may beemployed.

Gradients used in MRI may be generated by amplifiers that drive coils toproduce spatially varying magnetic fields oriented along a set ofphysical axes fixed to the MRI system geometry. A gradient subsystem maybe comprised of three amplifiers and corresponding coils, each setdirected along one of three perpendicular axes.

The gradient fields produced by the gradient amplifiers/coils may bedefined by “waveforms” (gradient level with respect to time) calculatedalong three “physical” perpendicular axes by an associated computer.When creating an image, the gradients that are required typically arespecified in the coordinate system of the image to be acquired; theseperpendicular left-right, up-down, and through-plane image directionscan be considered as a second set of “logical” coordinate axes (x′, y′,z′). These logical axes may not correspond to the physical axes on whichthe MRI system's gradient amplifiers/coils may be arranged, in order toallow for arbitrary imaging orientations. As a result, each logicalgradient waveform may be executed using a combination of one or more ofthe system's physically oriented gradients, depending on the desiredimaging orientation. When a pulse sequence is executed, the logicalgradient waveforms may be converted into physical gradient waveforms fordriving the gradient amplifiers on the MRI system. Such conversion maybe achieved by matrix rotation of the logical gradient waveforms.

The magnetic field gradient subsystem of an MRI system is critical indefining the utility of a scanner. In general, more powerful gradientsubsystems may provide greater applications capability. The power of agradient subsystem may refer to the limits on allowable gradientamplitude, allowable gradient slew rate, or some combination of the two.The gradient amplitude is the magnitude of linear magnetic fieldvariation that the gradient amplifiers produce in the gradient coils(typically expressed in Gauss per centimeter, G/cm), and the gradientslew rate is the rate at which the gradient amplifiers can change thegradient amplitude (typically expressed in G/cm per millisecond,G/cm/ms). For reference, various MRI scanners may be capable of maximumgradient amplitudes between 2 and 5 G/cm, and maximum slew rates between7 and 25 G/cm/ms.

In at least some circumstances, the attribute of importance in thegeneration of a gradient field pulse may be the integral of gradientamplitude over the duration of the gradient pulse (i.e., the gradientpulse area). This area may be desirable on either the physical orlogical axes, but is most typically specified along logical axes. Forexample, creating a linear phase distribution in tissues along a certainimage axis can be accomplished equivalently through generating a certaingradient area along that axis, roughly regardless of the particular waveshape that was used to generate that area. In other circumstances, thefirst moment of the pulse over time may also be important (e.g., theintegral of the gradient amplitude multiplied by time over the durationof the gradient pulse). This concern for areas and/or gradient momentsmay be utilized across a wide variety of MRI acquisition techniques,including, for example, slice-select refocusing, phase-encoding,velocity or flow compensation, crushing, spoiling, rewinding and readoutdefocusing gradient pulses. Since the shortest duration gradient pulseof a given area may provide the greatest flexibility in selecting pulsesequence echo time (TE) and pulse sequence repetition time (TR), it maybe desirable for the MRI system to produce these gradient pulses withthe minimum pulse duration possible given the prescribed pulse areaand/or moment.

Magnetic field gradients may be switched on and off during a pulsesequence to encode different positional information, to preparemagnetization, and to create steady states. Indeed, a large portion ofthe time required for MRI may include waiting for gradient waveforms toreach specified values (e.g., net area, moments, amplitudes) in thegradient hardware. Thus, the speed at which an MRI image may be producedmay directly depend on how quickly gradient waveforms can reach theirspecified values. Therefore, significant value may exist in computingtime-efficient gradient waveforms in a time efficient manner, as it mayhelp to minimize gradient switching times and, thus, the overall speedof image acquisition. Moreover, it may be beneficial to be able toquickly recalculate gradient waveforms, often in response to userinputs, such as selection of a new scan-plane geometry, adjusting imagefield-of-view, slice thickness, etc.

In addition to magnetic field gradients, other components of a pulsesequence may also be defined by a waveform. These components include,but are not limited to, the RF pulse used to excite nuclear spins andshims used to correct for inhomogeneities in the applied static magneticfield, B₀.

After the various waveforms necessary to complete an imaging sequenceare computed, they may be properly sequenced. For this process, aschedule (the “scheduler”) that accurately assembles the sequence ofwaveforms and other parameters that may be needed to execute a pulsesequence and a library of pre-determined waveforms may be uploaded intoa piece of sequencing hardware (the “sequencer”) memory for execution inthe respective sub-devices (e.g., gradients, RF coil, etc.) of the MRIsystem. Sequence events played during a pulse sequence may repeat,repeat with changes, repeat in a cycling manner, or be fairly differentfrom one to the next depending on the pulse sequence(s) used. As anexample, a real-time imaging application may desire to update the imagefield-of-view or RF tip angle dynamically in response to a user request(e.g., by moving the associated sliders in the user interface). The fullgamut of such changes could not be anticipated ahead-of-time, and thewaveforms and sequencer must be updated, the new sequence played, andthe data must be reconstructed and displayed all within hundreds ofmilliseconds in order for the user to perceive a responsive, low-latencyuser interface.

In current implementations known in the art, sequencer changes may onlyoccur at regular intervals during certain serial “dead-time” portions ofthe pulse sequence, where scheduler playback may not occur. Such aserial approach may introduce inefficiency into a pulse sequence, as aperiod of sequencer inactivity may be required for proper playback, andthe number of allowable changes per interval may be limited by theduration of the dead period. Moreover, any additional waveforms notknown prior to the start of sequence execution and, thus, not includedin the uploaded library may also require additional dead-periods foradditional waveform uploading. It should also be noted that in caseswhere sequencing occurs only during a dead-period, the flexibility ofthe sequencer to appropriately implement any unexpected waveform changesin real-time is limited.

This disclosure provides systems and methods for improving theperformance of magnetic resonance imaging (MRI) systems. The disclosurealso provides methods to generate magnetic field gradient waveforms thatmay be used in MRI, that may conform to hardware and safety constraintswith respect to gradient rate-of-change, that may be minimal duration,that may be developed in an efficient and intuitive interface, that maybe calculated efficiently, and that may be sequenced in a rapid,time-efficient manner that may be readily adaptable to unanticipatedchanges in a pulse sequence. Moreover, the sequencing methodology may beextended to any arbitrary waveform used in MRI.

Methods and systems of the disclosure may be advantageously fast tocompute, and arrive very or substantially nearly to the true optimalsolution that may be computed using much more time-consuming methods.Moreover, the approach may allow fast gradient pulses to be used acrossmost, if not all, MRI applications, including the design of pulsesequence applications where the multidimensional gradient area, moment,start, and end amplitudes may be the desired input parameters.

Time-Efficient Constrained MRI Gradient Waveforms

Magnetic field gradients may be a critical component of MRI scans, asthey are largely responsible for encoding spatial positions for creatingimages. These gradient fields in some cases may be switched on and offto encode different positional information, to prepare magnetization,and to create steady states. The speed at which these transitions canoccur may directly impact the overall speed of the MRI acquisition.

At least two independent limits may be applicable in determining howquickly gradient fields can be switched. A first independent limit maybe a physical hardware limit, which constrains the gradient slew rate toa specific value or range of values on each physical gradient axis.Further limits on the gradient parameters may be imposed by hardwareconstraints, including, but not limited to, physical heating of thegradient coils and/or amplifiers, performance characteristics of thegradient amplifiers, etc. A physical limit may exist for both gradientamplitude and also gradient slew rate. In the case of gradient slewrate, the allowable slew rate at any given instant may be a function ofthe gradient amplitude using for example the gradient “voltage model”known in the art. Further limits on the gradient parameters may beimposed by other hardware constraints, including, but not limited to,physical heating of the gradient coils and/or amplifiers, performancecharacteristics of the gradient amplifiers, etc.

A second independent limit may be a safety limit, as imposed byregulatory agencies. The safety limit may specify the maximum rate ofchange of magnetic field (dB/dt) that can be tolerated by a scan subject(e.g., patient), often based on a set of equations that describe theresponse of peripheral and cardiac nerve stimulation as a function ofdB/dt and pulse duration. As a result, the safety limit may depend uponthe size of the magnet or strength of the applied magnetic field,duration of the stimulus, and other factors. This is described in detailin IEC 60601-2-33, an international regulatory standard accepted by theU.S. Food and Drug Administration (FDA) and other regulatory bodies,which is entirely incorporated herein by reference. For instance, IEC60601-2-33 in page 30 describes controlling the gradient waveforms sothat the occurrence of intolerable peripheral nerve stimulation (PNS) inthe patient and the MR worker is minimized, and IEC 60601-2-33 in pages86-87 describes the calculation of an integrated maximum rate of changeof a magnetic field for the waveforms on each physical axis or as avector sum to limit PNS.

Each of the hardware limits may be expressed as a limitation on thegradient (G_(x), G_(y), and G_(z)) and gradient slew rate (i.e., thegradient rate-of-change—G′_(x), G′_(y), and G′_(z)) in each physicaldirection. In typically the most straightforward view of these hardwareconstraints, the hardware limits may be expressed as an absolute limitoperating on each of three Cartesian axes independently:

G_(x)<G_(x,max,hardware)

G_(y)<G_(y,max,hardware)

G_(z)<G_(z,max,hardware)

G′_(x)<G′_(x,max,hardware)

G′_(y)<G′_(y,max,hardware)

G′_(z)<G′_(z,max,hardware)

whereas the safety limit may be defined by an inseparable ellipticalconstraint, based on just the slew rate in each direction:

(w _(x) G′ _(x))²+(w _(y) G′ _(y))²+(w _(z) G′ _(z))² <G′ _(max,safety),

where w_(x), w_(y), and w_(z) represent axis-specific weighting factors.Using this model and considering only two dimensions, FIG. 1 depicts acombined constraint 100 of gradient hardware and safety limits. The box110 shown in FIG. 1 represents the hardware limit, the circle 120represents the safety limit, and the area of overlap (hatched region130) between the box and the circle represents a combined limit. Thecombined constraint shown in FIG. 1 may indicate the range of acceptablerates of change of gradients. In three dimensions, this range mayrepresent the region of intersection between a three-dimensionalellipsoid and a three-dimensional rectangular box.

If the gradient hardware is of low-performance, then the hardware limitmay not extend beyond the safety limit at any point, and a rectangularbox 110 representing the hardware limitation may be the overallconstraint. Conversely, for high-performance hardware, the hardwarelimit may exceed the safety limit in all directions and, thus, theoverall constraint may be the ellipsoid or circle 120 that defines thesafety limitation. Most often for a given system, though, the combinedconstraint falls between these two extremes. This may be due to thesignificant expense of gradient systems, as it may not be economicallyviable to engineer these systems to be capable of much more than theregulatory limit. Therefore, a complicated gradient waveformoptimization may be performed in order to minimize the time required forgradients to reach their desired values, and, thus, the speed of an MRIacquisition.

The optimization becomes more complicated still when the fullmathematical constraints are considered, where for the safety case, ahigher slew rate may be acceptable for a shorter duration, and for thehardware case, a higher gradient rate of change may be possible if thegradient magnitude is lower than its correctly biased full-scale.

Because these constraints do not follow a simple formula but rather aretypified by the piecewise, combined constraint as depicted in FIG. 1, itcan be quite challenging to derive a globally optimal solution undersuch a constraint, particularly when a larger number of desired waveformattributes must be simultaneously met. To arrive at a tractable, uniquesolution, a simplification may be desired.

To optimize gradients in a time-efficient manner under these constraintsusing methods provided herein, the gradient properties that may beneeded for a corresponding set of waveforms on each axis (e.g. x, y, andz) may be parameterized. Such properties may include the startinggradient magnitude (s_(x), s_(y,), and s_(z)), ending gradient magnitude(e_(x), e_(y,), and e_(z)), net gradient area (A_(x), A_(y,), andA_(z)), and various gradient moments (M_(n,x), M_(n,y,), and M_(n,z,)denoting the nth gradient moment). A subset of at least two of thesevalues may be specified on each axis to ensure a relevant solution. Forat least some imaging problems, these properties may represent thecomplete range of desired gradient manipulations.

For example, consider the typical 2-dimensional Cartesian readout designproblem 200 depicted in FIG. 2. The fundamental requirement of theCartesian readout 200 is the readout plateau, with a constant gradientamplitude on the Gx′ gradient axis for a specified duration (in thisexample, the duration is 1 ms and the amplitude is 2 G/cm). Prior tothat plateau, a so-called set of ‘prewinder’ gradients is necessary. Thewaveform shapes themselves are not important, but the waveforms muststart from zero amplitude on both axes and end with Gx′ at 2 G/cm andGy′ at 0. In addition, these gradients must have areas given by formulaeknown in the art; for the sake of example, say these are Ax′=−1 G/cm/msand Ay′=−1 G/cm/ms. Similarly, after the readout plateau, a set of‘rewinder’ gradients must be provided. In this example, they might bespecified with initial amplitudes sx′=2 G/cm, sy′=ex′=ey′=0, and the Y′rewinder gradient should have a total area of 1 G/cm/ms. In this case,the total area of the X′ rewinder is not of interest to us and can beleft unspecified. The design challenge would be to create the fastestset of gradient waveforms that meet all of these criteria. Such a set ofwaveforms is depicted at the right of FIG. 2. The following discussiondescribes how we might accomplish this design process.

The flow chart of FIG. 3 describes an embodiment of an iterative designprocess that may be used to rapidly design optimal and near-optimalgradient waveforms. The description in this paragraph is merely anoverview of the entire process; additional details will be provided overthe course of subsequent sections. As a first step 301, a set ofmultidimensional design constraints (sx′, sy′,, sz′, ex′, ey′,, ez′,Ax′, Ay′,, Az′, Mn,x′, Mn,y′,, Mn,z′, or some subset thereof) isdetermined using techniques in the art and based upon the requirementsof the imaging technique being employed. As a second step 302, ageometric transform parameter (to be used as a variable of iteration) isinitialized to some value. This initial value may be chosen at random ormay be selected based upon some heuristic or educated estimation basedupon the design constraints. As a third step 303, that geometrictransform parameter is used to arrive at a set of simplified designlimits Gmax and Smax, where the simplified limits conform to awell-defined geometric relationship such as a rectangular box orspheroid. As a fourth step 304, in the case of rotative transformationsdefined below, the design constraints are rotated into the rotativetransform space. As a fifth step 305, optimized waveforms are generatedusing these simplified constraints. As a sixth step 306, the resultantwaveforms are tested for equal length (or any other parameter that canbe left unfixed as a surrogate for length, such as relative gradientmagnitude, residual area, residual moment, duration of a sub-componentof the waveform, etc.). If all designed waveforms have equal length,then the iteration is considered finished; if not, then the geometrictransform parameter is appropriately updated (seventh step 307) and wereturn to step 303. After iteration completes, the resultant waveformsmay or may not be rotated in an eighth step 308 into a desiredcoordinate space—often, this involves transformation into physicalwaveforms to be used to drive the gradient hardware.

In some embodiments, parameterized gradient properties may begeometrically transformed into an alternative coordinate space, whichmay be denoted as a “rotative” space. This space may be denoted by axesa, b, and c. Gradient properties may be geometrically transformed withthe aid of systems of the disclosure, which can include one or morecomputer processors. To start, the geometric transformation betweenlogical axes (x′,y′,z′) and (a,b,c) may be arbitrarily chosen. In matrixnotation, each gradient property may be rotated using the rotationmatrix that specifies the geometric transformation between the(x′,y′,z′) and (a,b,c) coordinate systems. In this geometricallytransformed coordinate system, a safe set of gradient rate-of-changelimits, inscribed within the original combined constraint, may bedefined that represents the maximum separable gradients possible giventhe combined constraint. A separable constraint is represented by arectangle (2D) or rectangular box (3D) oriented in the (a,b,c) space.The dimensions of this box should be chosen to ensure that no portion ofthe box exceeds the combined original constraint, while maximizingeither the area of the box, the combined axis lengths, or some othersize metric on the box. Preferentially, the area of the box should bemaximized such that it is inscribed within the combined constraint.

For example, if the rate-of-change limits for a given geometricallytransformed space are constrained by a spherical safety limit|SRmax,safety| alone, then a separable constraint for that situationcould be described by

${{SR}_{\max,a} = {{SR}_{\max,b} = {{SR}_{\max,c} = \frac{{SR}_{\max,{safety}}}{\sqrt{3}}}}},$

where the maximum slew rates on each axis here have been chosen suchthat they are equal to one another. An example of the application of asimilar constraint for two dimensions is shown in FIG. 2.

In this example, the (a,b) coordinate system is rotated by an angle □from the logical (x′,y′) system. In this particular example, therotation matrix is

$\begin{bmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{bmatrix}\quad$

and points (x′,y′) in the logical space can be geometrically transformedinto the (a,b) space using the matrix equation:

$\begin{bmatrix}a \\b\end{bmatrix} = {{\begin{bmatrix}{\cos \mspace{14mu} \theta} & {{- \sin}\mspace{14mu} \theta} \\{\sin \mspace{14mu} \theta} & {\cos \mspace{14mu} \theta}\end{bmatrix}\begin{bmatrix}x^{\prime} \\y^{\prime}\end{bmatrix}}.}$

In this example, the separable constraint is dictated by the globalsafety constraint given by

SR _(max,a) ² +SR _(max,b) ² ≤SR _(max,safety) ²,

the separable-constraint area is maximized by an inscribed square withside length given by

${SR}_{\max,a} = {{SR}_{\max,b} = {\frac{{SR}_{\max,{safety}}}{\sqrt{2}}.}}$

Note that the square root here differs from the above equation becauseit is a two-dimensional example.

In the coordinate space of the rotated box, side lengths are constrainedso that each corner vertex intersects with the global safety constraint.In one example of geometrically transformed spaces 400 shown in (a) ofFIG. 4, the allowed gradient rates of change in the geometricallytransformed space correspond to the dark shaded region of the rotatedbox circumscribed by the safety limit circle. For the sake ofsimplicity, the coordinate space in (a) has been set so that logical andphysical coordinate systems are the same (x,y,z) =(x′,y′,z′). The moregeneral case, where logical and physical coordinates are not coincident,is shown in (d) of FIG. 4.

In other embodiments, a geometrically transformed space may be chosenthrough proportionate selection of limits along the cardinal logicalaxes rather than by an additional rotation. This case, depicted in (b)of FIG. 4 for the simplified case where logical and physical coordinatesare equivalent, permits the selection of unique limit maxima along eachlogical axis. In the case of gradient magnitude limits, these could bedenoted with (Gmax,x′, Gmax,y′, Gmax,z′) and in the case of slew-ratelimits, (SRmax,x′, SRmax,y′, SRmax,z′). To facilitate creation of thistype of geometric transform and later iteration, an angle □ may beselected as shown in (b), and the corner of the box chosen to conform tothe minimum limit at that angle from the origin. For the example shown,with safety limits being the operable limit in that case, the limitswould be:

SR _(max,x′)=2|SR _(max,safety) sin (ϕ|

SR _(max,y′)=2|SR _(max,safety) cos (ϕ)|

A more generalized case for this type of geometric transformation, wherelogical and physical coordinate axes are not equivalent, is shown in (e)of FIG. 4. Note that in this geometric transformation, the axes of thebox do not rotate along with the physical axes and therefore a differentset of limits may be operative. In the case depicted, the new logicalframe leads to new limits that are dictated by the hardware slew limitsrather than the safety limits.

In still other embodiments, a simplifying geometric transform may beapplied that limits created gradients based upon a magnitude orspheroidal constraint. This case is depicted for two dimensions in (c)of FIG. 4 for coincident logical and physical axes, and in (f) of FIG. 4for unequal logical and physical axes. For a spheroidal constraint, axesof the spheroid may be chosen along physical axes x,y,z in which casethe slew rate constraint would be:

${\frac{{SR}_{x}^{2}}{{\min \left( {{SR}_{x,\max,{hardware}},\frac{{SR}_{\max,{safety}}}{w_{x}}} \right)}^{2}} + \frac{{SR}_{y}^{2}}{{\min \left( {{SR}_{y,\max,{hardware}},\frac{{SR}_{\max,{safety}}}{w_{y}}} \right)}^{2}} + \frac{{SR}_{z}^{2}}{{\min \left( {{SR}_{z,\max,{hardware}},\frac{{SR}_{\max,{safety}}}{w_{z}}} \right)}^{2}}} \leq 1$

This choice of constraint may not allow separable design as the gradientlimits in one axis are affected by gradients on the other axes. However,well defined solutions for common problems exist for spheroidalconstraints, so in many cases a closed-form solution exists. As anexample, take the simplified 2D case depicted in (c) or (f). Because thehardware constraint is smaller than the safety constraint on bothphysical axes, |SR_(max)|=SR_(max,hardware). Using this magnitudetransformation, a set of optimized waveforms for the readout rewinder ofFIG. 2 can be derived. On the x′ axis, the length of the final waveformis given by

${\frac{s_{x^{\prime}}}{{SR}_{x^{\prime}}} = L},$

where L is the length of the waveform and SR_(x′) ²+SR_(y′)²≤SR_(max,hardware) ² as a result of applying the above slew rateconstraint equation, and noting that the slew rate constraints can beapplied in the logical frame because of the circular constraintboundary. On the y′ axis, a similar equation for L can be derivedassuming a triangular waveform:

$2\sqrt{\frac{A_{y^{\prime}}}{{SR}_{y^{\prime}}} = {T.}}$

It is often desired these times T to be equal on all axes, so settingthese equations equal to one another and solving for SRy′ results in:

${SR}_{y^{\prime}} = {\frac{- s_{x^{\prime}}^{2}}{8A_{y^{\prime}}} + {\sqrt{\frac{s_{x^{\prime}}^{4}}{64A_{y^{\prime}}^{2}} + {SR}_{\max,{hardware}}^{2}}.}}$

Assuming a SRmax,hardware of 9.5 G/cm/ms and other parameters from FIG.2, this equation can be solved to find SRy′=8.99 G/cm/ms and SRx′=3.08G/cm/ms. These slew rates lead to waveforms with total duration T=0.65ms. Note that in this solution, iteration was not required to arrive ata solution with equal durations on all axes.

The choice between these three geometric transform spaces may bearbitrarily made, and indeed the optimized gradients that result areoften similar in performance. The proportional transformation (in (b)and (e)) can be advantageous because it allows for post-hoc scaling oflogical gradient waveforms. More specifically, often a gradient scalingoperation occurs from repetition to repetition along a specific axis, asmay typically occur in Cartesian phase-encoding gradients known in theart. These phase-encoding gradients would typically be implemented byscaling (reducing) gradients along the logical Gy′ axis while leavingthe Gx′ magnitude unaltered. Looking at point P in (d), one can see thatsuch a Gy′ reduction without changing Gx′ could easily lead to aparameter value outside of the allowable combined constraint.Conversely, when using the proportional or magnitude transformationapproaches, any scaling along x′ and y′ axes can be accommodated and iscertain to be within the combined constraint. Thus, this method is moregenerally useful in cases where gradient scaling is desired after thegradient-design stage. Furthermore, the proportional and magnitudemethods are more amenable to composing gradients where different typesof limits are desired on different axes, like having a gradient areaconstraint on one axis but only gradient start and end constraints onother logical axes. The operation of geometrically transforming theconstraints cannot be efficiently performed in the rotative-transformspace.

Regardless of the transform space chosen (rotative, proportional, ormagnitude), time-optimal gradient waveforms may be calculated byiterating over the full range of its transform parameter (θ for rotativetransforms, or ϕ for proportional ones; iteration may or may not benecessary for magnitude transforms). A flowchart of the process 300 isgiven in FIG. 3.

The combined constraint with respect to the geometrically transformedspace may be solved symbolically for each case where some subset ofareas, gradients, start, and end magnitudes are desired.

As an example, consider again the Cartesian Readout of FIG. 2. To designthe rewinder block, a simple ramp is required on the X′ axis, and atrapezoid or triangle is required on Y′. The duration of the X′ ramp canbe calculated for a known slew rate SRx′ using

$T_{x^{\prime}} = {\frac{s_{x^{\prime}} - e_{x^{\prime}}}{{SR}_{x^{\prime}}}.}$

Using the values in the example and given a slew rate SRx′=3 G/cm/ms,the duration Tx′ for this ramp iteration would be ⅔ ms. Note that thisresult is extremely similar to the result determined using the magnitudetransformation above.

On the Y′ axis, a specified area Ay′ is needed, so a simple ramp is notsufficient. Assuming a triangle waveshape would suffice, the area ofwhich can be derived as

$A_{y^{\prime}} = {\left( {\frac{s_{y^{\prime}}}{2} + \left( {s_{y^{\prime}} + {{SR}_{y^{\prime}}\frac{T_{y^{\prime}}}{2}}} \right) + \frac{e_{y^{\prime}}}{2}} \right){\frac{T_{y^{\prime}}}{2}.}}$

Rearranging terms and using the quadratic formula to solve for Ty′, wearrive at

$T_{y^{\prime}} = {\frac{{3s_{y^{\prime}}} + e_{y^{\prime}}}{2{SR}_{y^{\prime}}} \pm {\frac{\sqrt{\left( \frac{{3s_{y^{\prime}}} + e_{y^{\prime}}}{2} \right)^{2} + {4A_{y^{\prime}}{SR}_{y^{\prime}}}}}{{SR}_{y^{\prime}}}.}}$

For the values in the example and given a slew rate SRy′=9 G/cm/ms, theduration Ty′ for this iteration would be ⅔ ms. As this is identical tothe duration found for Tx′, an optimal solution has been found and theiteration would be ceased at this point.

The result of this calculation may be a set of gradient waveforms foreach geometrically transformed axis. If desired, these waveforms can begeometrically transformed back into logical or physical coordinatespaces using a rotation matrix approach similar to that described above.

In some embodiments, if the durations of the set of gradient waveformson each transformed axis are equal to each other, then it may bedetermined that a minimum time solution has been found. However, if thegradient waveforms have different durations on any axis, then animproved solution may exist at a different rotation angle. To find thisangle, a new selection of transform parameter can be selected, and thesame procedure may be repeated until an acceptable solution is found.Once a minimum time solution has been found, the calculated waveforms inthe geometrically transformed space may then be geometricallytransformed back to the physical space to drive the MRI system'sgradient hardware.

The required degree of rotation for the geometrically transformed spacethat may be searched for an optimal solution may be limited to only onequadrant of the circle (in the two-dimensional example, 0-90 degrees)shown in FIG. 4, or one eighth of the space of solid angles in the3-dimensional case In some cases, the target function of differencesbetween gradient durations may be well-behaved and smooth, meaning thata rapid nonlinear iterative solution solver can be applied. A binarysearch implementation can be made to find the best solution within atleast about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, or 100iterations. In some examples, a best solution may be found within atmost about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 100, 200,300, 400, 500, or 1000 iterations. In some cases, a nonlinear iterativesearch algorithm, such as conjugate gradient descent, Krylov subspacemethods, and others can be used. Commonly used implementations can befound in MATLAB, C, C++, and other programming languages. A nonlineariterative search algorithm may be suited for three-dimensionalsolutions, where the additional degree of freedom in the solution mayrender a binary search inefficient.

FIG. 5 shows the physical gradients designed by methods of thedisclosure as a function of time, for a case in three-dimensions. FIG. 6shows the point-wise gradient change limits for the waveform of FIG. 5.Solid straight lines at x=+−15 G/cm/msec and y=+−15 G/cm/msec representhardware limitations specified for this example. Curved solid linesrepresent maximum safe rates of change due to regulatory limitations.Many of the data points reside near one boundary or the other, most datapoints are at the theoretical limit, and the average data point is atabout 93% of that limit. A truly optimal waveform would be at 100%. Themethods described herein can thereforecome very close to the theoreticalideal while taking very little time to calculate.

Methods and systems of the disclosure may be used for nonlinear magneticfield gradients, in which the constraint space may be more difficult todescribe than the geometric shapes shown here.

Additional special constraints may be used depending on how theresulting gradient is expected to be used. For example, if the gradientmust be freely rotatable so that it can be used in any scan-planeorientation, then constraints may be limited to a spherical spaceinscribed into the existing combined constraint. As previouslydiscussed, it may be desirable for one or more of the gradient axes tobe scaled down independently, in which case that scaling may result inexceeding limits on another axis. Use of either the proportional ormagnitude/spheroidal optimization methods can avoid this difficulty.This may be of concern when designing gradients to be used inphase-encoding, unless separate optimizations are to be used for eachphase-encoding step.

This technique may converge quickly. In some examples, this techniquemay converge is a time period of at least about 1, 2, 3, 4, 6, 7, 8, 9,10, 15, 20, 30, 40, 50, or 60 seconds or 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,15, 20, 30, 40, 50, or 60 minutes or 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12,18, or 24 hours. This technique may also not be computationallyintensive and may also be sped up by further parallelization of thecomputation steps. In particular, multiple values of the transformparameter could be independently analyzed, effectively parallelizingsteps 3 through 6 in FIG. 3. Parallelization may be particularly usefulin a three-dimensional computation. A good initial estimation (or seed)for the geometric transformation between the physical space and thegeometrically transformed space may also greatly speed up thecomputation. This may be accomplished through heuristic algorithms basedupon the gradient parameters to be optimized.

For example, if areas Ax′, Ay′, and Az′ are desired, an initial guessfor slew rate limits and gradient limits along these axes might be a setof parameters that are scaled proportionally to the relative sizes ofthe desired areas:

${{SR}_{i} \propto \frac{A_{i}}{\sqrt{A_{x^{\prime}} + A_{y^{\prime}} + A_{z^{\prime}}}}},$

where i represents each of x′, y′, and z′.

The technique described above may be further optimized by combiningiterations for different types of geometric transformations (e.g.,rotative and proportional). In other words, both rotative andproportional solutions might be obtained, and the fastest of the twochosen for use. In this case, the additional optimizations may take verylittle time if the solution from the other transformation type is usedas a starting point for the next type of iteration. Otherwise, theiteration may proceed as in the original case.

The ability to produce multidimensional optimized gradients with givenstart and end amplitudes, areas, and moments may also be incorporatedinto a graphical tool for MRI pulse-sequence designers (or systems) torapidly and flexibly produce pulse sequences. Such a tool may bepresented as a graphical user interface of the system. Such a tool mayprovide the ability to arbitrarily place pulse blocks with givenamplitudes, areas, and moments, and to specify their temporalrelationships to one another. In such a case, the ability to rapidlycompute new optimized gradients may be essential to providing immediatefeedback to the user in response to parameter changes.

In addition to peak slew rate limitations, alternative or additionalgradient safety limits may be applied. For example, in the so-called“fixed-parameter” mode of MRI scanning for use on patients withindwelling metallic implants, additional constraints on peak gradientslew rate and root-mean-square (RMS) gradient slew rate may be applied.These additional constraints may be incorporated into the separabledesign process and similarly used to arrive at an efficient set ofwaveforms given the combination of all applied constraints. Similarly,these additional constraints could be applied on patients undergoinginterventional procedures using metallic catheters, guidewires, andother interventional devices.

While the techniques of the disclosure may have greatest application inthe design of waveforms by specified area, moments, and start and endamplitudes, there may also be the possibility of creating specifick-space trajectories via the same techniques. k-Space is the term forthe format in which MRI raw data is initially collected. This raw datamust undergo a Fourier transform in order to convert it to image data.Locations traversed in k-space are proportional to the net integratedarea under the gradient waveforms; thus, specifying gradients by theirnet area can directly lead to traversal of a desired k-space trajectory.Sampling may be performed along simple trajectories that allow for atrivial solution and shorter scan times. For example, such k-spacesampling may be along parallel lines.

More complicated sampling trajectories may be advantageous, but oftenmay also require nontrivial solutions and, thus, longer scan times. Forexample, a spiral k-space trajectory, first proposed by both Likes (U.S.Pat. No. 4,307,343) and Ljunggren (JOURNAL OF MAGNETIC RESONANCE S4,338-343 (1983)), can imply a specific area requirement for arriving ateach k-space location. Spiral scans may be an efficient way to coverk-space and may be particularly advantageous in the presence of adynamic environment such as in the heart or flowing blood.

There are a number of gradient waveforms that may trace out a particularspiral k-space trajectory. The design of these gradient waveforms may bean important element of spiral scanning, and a number of iterative andnon-iterative approaches (e.g., U.S. Pat. No. 6,020,739) have beensuccessfully applied to this problem. Again, however, these approachesmay be time consuming to implement and not readily amenable to real-timeimaging.

To arrive at a spiral trajectory in a time-efficient manner using thedisclosed methods, the k-space sampling step may be set as finely asdesired for accurate trajectory fidelity. Then, starting from the firstk-space sample (e.g., at the k-space origin), separate optimizationprocedures may be used to step from the previous k-space location to thenext locations. At each step, the start amplitude may be specified asthe ending amplitude of the previous step, and the end amplitude may beleft unconstrained. In the final step, a rewinder (the trajectorysegment that connects the end of the spiral with the origin) may bedesigned with zero end amplitude and sufficient area to refocus to thek-space origin.

Waveform Switching

MRI may require the rapid uploading of sets of arbitrary waveforms, thatinclude waveforms for gradients, radiofrequency (RF) channels, shims,and/or fields into a piece of dedicated MR sequencing hardware that maybe limited in processing power and/or available memory. Parameters ofthese waveforms such as their durations, amplitudes, data points, andnumber all may change arbitrarily and may not be known ahead of time.

While memory and computation power may be getting cheaper, sequencerhardware systems tend to be memory and processor-limited. For example,it may be impractical to provide enough on-board memory on theseprocessors to contain all the samples needed to sequence an entire2-hour scan with 5 16-bit data channels at 500 kHz (˜32 GB of memory).Even if the memory itself were not a limitation, the time required totransfer these amounts of data may prohibit real-time sequencingchanges.

MR imaging sequences, though, may consist of a high degree ofrepetition. Therefore, vastly smaller chunks of waveform and associatedparameter data may be uploaded to the sequencing hardware along with aschedule of instructions for the order and amount of repetition requiredfor proper playback. This type of simple compression may reduce memoryrequirements, even for very long scans. Because of processinglimitations, the method for compression may be through per-axis waveformschedulers, shown in conceptual form in FIG. 7.

As shown in FIG. 7, uploaded schedulers 710 may be “played” for eachwaveform axis as a sequence is executed. The schedulers may provide alist of pointers to waveforms in the uploaded waveform library 710, sothat waveform sections that may need to be repeated are only storedonce. The scheduler may also: execute simple ‘geometric transformations’on any waveform in the library, including bulk amplitude changes,duration changes, phase/rotation changes; change the waveform pointer topoint at a different location in the waveform library; or schedule delayelements.

Serial sequencing 800A is shown in FIG. 8a . Each axis' scheduler mayexecute until it reaches the end of its sequence of instructions forplayback. Additional time may then be reserved for updating thescheduler with any changes to the set of waveforms parameters. Thecomplete cycle (playback+scheduler updating), occurs over a timeinterval TR and repeats itself with the updated scheduler being playedat the start of the next cycle. This allows for basic MRI sequencing andmay provide all the functions needed for scanning when all of thepossible scan parameters are known in advance. Serial sequencing, asdescribed herein, may be combined with or modified by U.S. Pat. Nos.7,053,614, 7,102,349, and 5,465,361, which are entirely incorporatedherein by reference.

The method of FIG. 8a may not be capable of addressing changingwaveforms and sequence timings based upon arbitrary external events,such as changes entered via user input. In this case, it may be that noamount of change to the scheduler can provide the unanticipated newwaveform that is needed—additional waveform uploading, and, thus,additional sequencing time may be required. Furthermore, the serialnature of the scheduler update after each playback period (FIG. 8a )indicates that scan efficiency may be compromised, as all sequencers maybe inactive during scheduler updating. In order to keep TR to a minimum,the serial nature of sequencing may also limit the amount of schedulerchanges that can practically be accomplished during each TR interval. Topermit faster changes to arbitrary waveforms during active scanning,another method is needed.

This disclosure provides systems and methods 800B for buffering changesto the scheduler and waveform libraries while keeping the existinghardware structure and memory layout, as shown schematically in FIG. 8b. Additional memory may be allocated within the sequencer to permitbuffering of all scheduler updates and associated waveforms. While oneTR of waveforms is being played from an active memory region, thescheduler and waveform library for a future TR may be updated into thebuffer memory.

At the end of one TR, the active memory region under playback may beswapped with the buffer memory region containing the next updates to beplayed. Depending on hardware limitations, this swap may require a shortperiod of sequencer inactivity, or it may be possible to perform thisswap atomically, in which case no period of sequencer inactivity isrequired. In the case of atomic swapping, then full-duty-cycle waveformplayback may be achieved while allowing for arbitrary changes insequences to be driven by the external host computer.

Each TR interval may be broken into one or more sub-intervals, calledblocks to facilitate fast changes to waveforms. For example, FIG. 9shows one TR 900 of a spiral flow-encoded pulse sequence wherein threelogical functions are sequentially completed: slice selection, flowencoding, and spiral readout. These blocks may or may not be dividedinto separate sub-blocks (labeled Block 1, Block 2, and Block 3 here).Blocks may contain logical elements of the pulse sequence that include,but are not limited to, an inversion pulse or flow-encoding gradients.Moreover, several logical functions may be combined into one block.Real-time changes such as rotations, scaling, and enabling/disabling maybe performed at the block level, allowing the pulse sequence designerthe ability to precisely define the scope of any anticipated change.

While the present technique may allow for uploading and playback ofarbitrary waveforms at any time, it may also be combined with one ormore conventional methods (e.g., providing special functions forwaveform scaling, rotations, phase modifications, etc.) to allow a morelimited set of modifications at the sequencer level. This may permitbackward compatibility with existing applications that may require suchoperations to be present on the sequencer. Moreover, it may also be moreefficient to perform such waveform transformations without re-uploadingthe waveforms to the sequencer.

If the computer servicing the buffer memory is unable to achievereal-time response, then a longer buffer of queued TRs may be desired.The technique may be adapted to create a longer waveform and schedulerqueue that permits the waveform-generating computer to have periodicintervals of slower responsiveness. If this buffer were implemented as astandard first-in-first-out (FIFO) queue, then any asynchronous changesto the sequence may be delayed by a time corresponding to the buffer'slength. To prevent this latency, the buffer may be safely flushedwhenever an unanticipated change occurs. Flushing the queue from the endand going backward may allow the fastest possible change while allowingfor potential computer slowdowns.

As an example, during a spiral-scanning MRI experiment, the user maydesire to acquire a higher resolution or a different field-of-view. Suchalterations to the pulse sequence may necessitate a change to the spiralreadout trajectory that may not have been anticipated prior to scanning.Other systems presently available may not permit changes to the waveformlibrary after the start of a scan, and, thus, may not allow the requiredchange to the spiral readout trajectory. These changes may be permitted,however, with architecture of the present invention as a buffer memoryregion exists for storing the waveforms needed to change the spiralreadout trajectory prior to playback. In addition, such new waveformsmay also have different lengths and other associated parameters, whichmay require updates to the scheduler which can also be generated in thebuffer memory region prior to playback.

In another example, the present invention may allow an imaging sequenceto autonomously adapt to conditions based upon image features of prioracquired real-time data. If prior real-time images indicate that thefield-of-view is too small for the area being displayed, alternativespiral waveforms may be generated and substituted into the imagingsequence in real-time.

In yet another example, spiral trajectory corrections based uponeddy-current estimates may be pushed to the sequencer in real-timeduring scanning, rather than stopping the imaging sequence, making thecorrections, and restarting.

The present invention may allow more time to be dedicated to schedulerand waveform updates, without increasing the total scan time and alsomay permit any sequence to be played as long as the respective updaterequired for desired playback can be computed faster than TR. Inaddition, an interrupt or other standard concurrency technique (e.g.,mutex, semaphore, etc.) may be used to adaptively set the sequencerepetition time to accommodate whatever time is required to sequence thenext interval by extending the current TR or by interjecting atransitional TR interval.

Moreover, the methods and systems disclosed herein may also allow allaspects of the sequence to be changed, including, but not limited to,the waveforms in the uploaded library, sequence timings, and number ofwaveform pulses.

Moreover, methods of the disclosure may be applied on any scanner (e.g.,MRI scanner) that uses two-level scheduler and waveform libraries. Atthe present time, most scanners use such architecture as a part of theirsequencing hardware.

Systems

This disclosure provides computer system that may be programmed orotherwise configured to implement methods provided herein.

FIG. 10 schematically illustrates a system 1000 comprising a computerserver (“server”) 1001 that is programmed to implement methods describedherein. The server 1001 may be referred to as a “computer system.” Theserver 1001 includes a central processing unit (CPU, also “processor”and “computer processor” herein) 1005, which can be a single core ormulti core processor, or a plurality of processors for parallelprocessing. The server 1001 also includes memory 1010 (e.g.,random-access memory, read-only memory, flash memory), electronicstorage unit 1015 (e.g., hard disk), communications interface 1020(e.g., network adapter) for communicating with one or more othersystems, and peripheral devices 1025, such as cache, other memory, datastorage and/or electronic display adapters. The memory 1010, storageunit 1015, interface 1020 and peripheral devices 1025 are incommunication with the CPU 1005 through a communications bus (solidlines), such as a motherboard. The storage unit 1015 can be a datastorage unit (or data repository) for storing data. The server 1001 isoperatively coupled to a computer network (“network”) 1030 with the aidof the communications interface 1020. The network 1030 can be theInternet, an internet and/or extranet, or an intranet and/or extranetthat is in communication with the Internet. The network 1030 in somecases is a telecommunication and/or data network. The network 1030 caninclude one or more computer servers, which can enable distributedcomputing, such as cloud computing. The network 1030 in some cases, withthe aid of the server 1001, can implement a peer-to-peer network, whichmay enable devices coupled to the server 1001 to behave as a client or aserver. The server 1001 is in communication with a imaging device 1035,such as a magnetic resonance imaging (MRI) device or system. The server1001 can be in communication with the imaging device 1035 through thenetwork 1030 or, as an alternative, by direct communication with theimaging device 1035.

The storage unit 1015 can store files, such as computer readable files(e.g., MRI files). The server 1001 in some cases can include one or moreadditional data storage units that are external to the server 1001, suchas located on a remote server that is in communication with the server1001 through an intranet or the Internet.

In some situations the system 1000 includes a single server 1001. Inother situations, the system 1000 includes multiple servers incommunication with one another through an intranet and/or the Internet.

Methods as described herein can be implemented by way of machine (orcomputer processor) executable code (or software) stored on anelectronic storage location of the server 1001, such as, for example, onthe memory 1010 or electronic storage unit 1015. During use, the codecan be executed by the processor 1005. In some cases, the code can beretrieved from the storage unit 1015 and stored on the memory 1010 forready access by the processor 1005. In some situations, the electronicstorage unit 1015 can be precluded, and machine-executable instructionsare stored on memory 1010. Alternatively, the code can be executed on aremote computer system.

The code can be pre-compiled and configured for use with a machine havea processer adapted to execute the code, or can be compiled duringruntime. The code can be supplied in a programming language that can beselected to enable the code to execute in a pre-compiled or as-compiledfashion.

Aspects of the systems and methods provided herein, such as the server1001, can be embodied in programming. Various aspects of the technologymay be thought of as “products” or “articles of manufacture” typicallyin the form of machine (or processor) executable code and/or associateddata that is carried on or embodied in a type of machine readablemedium. Machine-executable code can be stored on an electronic storageunit, such memory (e.g., read-only memory, random-access memory, flashmemory) or a hard disk. “Storage” type media can include any or all ofthe tangible memory of the computers, processors or the like, orassociated modules thereof, such as various semiconductor memories, tapedrives, disk drives and the like, which may provide non-transitorystorage at any time for the software programming. All or portions of thesoftware may at times be communicated through the Internet or variousother telecommunication networks. Such communications, for example, mayenable loading of the software from one computer or processor intoanother, for example, from a management server or host computer into thecomputer platform of an application server. Thus, another type of mediathat may bear the software elements includes optical, electrical andelectromagnetic waves, such as used across physical interfaces betweenlocal devices, through wired and optical landline networks and overvarious air-links. The physical elements that carry such waves, such aswired or wireless links, optical links or the like, also may beconsidered as media bearing the software. As used herein, unlessrestricted to non-transitory, tangible “storage” media, terms such ascomputer or machine “readable medium” refer to any medium thatparticipates in providing instructions to a processor for execution.

Hence, a machine readable medium, such as computer-executable code, maytake many forms, including but not limited to, a tangible storagemedium, a carrier wave medium or physical transmission medium.Non-volatile storage media include, for example, optical or magneticdisks, such as any of the storage devices in any computer(s) or thelike, such as may be used to implement the databases, etc. shown in thedrawings. Volatile storage media include dynamic memory, such as mainmemory of such a computer platform. Tangible transmission media includecoaxial cables; copper wire and fiber optics, including the wires thatcomprise a bus within a computer system. Carrier-wave transmission mediamay take the form of electric or electromagnetic signals, or acoustic orlight waves such as those generated during radio frequency (RF) andinfrared (IR) data communications. Common forms of computer-readablemedia therefore include for example: a floppy disk, a flexible disk,hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD orDVD-ROM, any other optical medium, punch cards paper tape, any otherphysical storage medium with patterns of holes, a RAM, a ROM, a PROM andEPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wavetransporting data or instructions, cables or links transporting such acarrier wave, or any other medium from which a computer may readprogramming code and/or data. Many of these forms of computer readablemedia may be involved in carrying one or more sequences of one or moreinstructions to a processor for execution.

The server 1001 can be configured for data mining, extract, transformand load (ETL), or spidering (including Web Spidering where the systemretrieves data from remote systems over a network and access anApplication Programmer Interface or parses the resulting markup)operations, which may permit the system to load information from a rawdata source (or mined data) into a data warehouse. The data warehousemay be configured for use with a business intelligence system (e.g.,Microstrategy®, Business Objects®).

The results of methods of the disclosure can be displayed to a user on auser interface (UI), such as a graphical user interface (GUI), of anelectronic device of a user, such as, for example, a healthcareprovider. The UI, such as GUI, can be provided on a display of anelectronic device of the user. The display can be a capacitive orresistive touch display. Such displays can be used with other systemsand methods of the disclosure.

Methods and systems of the disclosure may be combined with or modifiedby other methods and systems, such as those described in U.S. Pat. Nos.5,512,825, 6,020,739, 6,198,282, 7,301,341, 5,465,361, 7,102,349, and7,053,614, which are entirely incorporated herein by reference.

It should be understood from the foregoing that, while particularimplementations have been illustrated and described, variousmodifications can be made thereto and are contemplated herein. It isalso not intended that the invention be limited by the specific examplesprovided within the specification. While the invention has beendescribed with reference to the aforementioned specification, thedescriptions and illustrations of the preferable embodiments herein arenot meant to be construed in a limiting sense. Furthermore, it shall beunderstood that all aspects of the invention are not limited to thespecific depictions, configurations or relative proportions set forthherein which depend upon a variety of conditions and variables. Variousmodifications in form and detail of the embodiments of the inventionwill be apparent to a person skilled in the art. It is thereforecontemplated that the invention shall also cover any such modifications,variations and equivalents. It is intended that the following claimsdefine the scope of the invention and that methods and structures withinthe scope of these claims and their equivalents be covered thereby.

What is claimed is:
 1. A method of generating a multi-dimensionalgradient waveform for use in a magnetic resonance imaging (MRI) devicecoupled to a computer system, the method comprising: (a) providing a setof design constraints for the multi-dimensional gradient waveform alongeach dimension of the multi-dimensional gradient waveform, wherein theset of design constraints comprise a gradient start amplitude and agradient end amplitude; (b) providing one or more of (i) a set ofhardware limitations for maximum gradients achievable by the MRI device,the set of hardware limitations comprising a maximum gradient slew-rateon each physical axis of the MRI device and a maximum gradient amplitudeon each physical axis, or (ii) a set of regulatory limitations formaximum gradient fields that may be safely applied to a scan subject,the set of regulatory limitations comprising a maximum safe rate ofchange of a magnetic field of the MRI device for the scan subject; (c)applying, with the aid of the computer processor, one or more geometrictransformations to the set of design constraints, and also to the set ofhardware limitations or the set of regulatory limitations, therebyplacing the design constraints, and also the hardware limitations or theregulatory limitations, in a geometrically transformed coordinate space;(d) generating, with the aid of the computer processor, themulti-dimensional gradient waveform by calculating a gradient waveformfor each gradient dimension (i) that simultaneously satisfies all of thedesign constraints, and also the hardware limitations or regulatorylimitations, in the geometrically transformed coordinate space and (ii)where each dimension of the gradient waveform meets an equal lengthcondition of having the same time length as all other dimensions of thegradient waveform; and (e) generating a magnetic field gradient pulse,with the MRI device, according to criteria of the multi-dimensionalgradient waveform of step (d).
 2. The method of claim 1, wherein themulti-dimensional gradient waveform generated encompasses two or threegradient axes, respectively corresponding to a plane or volume inCartesian space.
 3. The method of claim 1, wherein the set of designconstraints further comprises one or more of a gradient area, a gradientfirst moment, or a higher order gradient moment.
 4. The method of claim1, wherein one or more of the maximum gradient amplitude or maximumgradient slew-rate limit is calculated as a peak or as aroot-mean-square limit.
 5. The method of claim 1, wherein the regulatorylimitation is configured to limit induced tissue currents in the scansubject and minimize intolerable peripheral nerve stimulations in thescan subject.
 6. The method of claim 1, wherein the regulatorylimitation comprises an integrated maximum rate of change of a magneticfield (dB/dt) for the waveform on each physical axis or as a vector sum.7. The method of claim 1, wherein the regulatory limitation comprises amaximum root-mean-square gradient slew rate.
 8. The method of claim 1,wherein the one or more geometric transformations is a spatial rotation,with the spatial rotation comprising one or more of a planar rotation, athree-dimensional rotation, or a vector rotation.
 9. The method of claim8, wherein step (e) further comprises performing an inversetransformation of the multi-dimensional gradient waveform back into anative coordinate system of the MRI device.
 10. The method of claim 1,wherein one or more geometric transformations is rotative, proportional,or an increase or decrease in magnitude.